IJPAM: Volume 108, No. 4 (2016)

GEOMETRIC PROPERTIES FOR INTEGRO-DIFFERENTIAL
OPERATOR INVOLVING THE PRE-SCHWARZIAN
DERIVATIVE

Zainab E. Abdulnaby$^{1,2}$, Adem Kilicman$^1$, Rabha W. Ibrahim$^3$
$^1$Department of Mathematics
Faculty of Science
Universiti Putra Malaysia
43400 UPM, Serdang, Selangor, MALAYSIA
$^2$Department of Mathematics
College of Science
Al-Mustansiriyah University
Baghdad, IRAQ
$^3$Faculty of Computer Science and Information Technology
University Malaya
50603, MALAYSIA


Abstract. Recently, the study of operators theory (differential, integral, integro-differential) has been increased. It appears widely in the geometric function theory, to create some generalized subclasses of analytic functions. In this effort, we introduce a generalized integro-differential operator $ \mathfrak{J}_{m}(z)$ and obtain its properties by utilizing the pre-Schwarzian derivative. Applications are illustrated, based on fractional calculus in the sequel.

Received: March 26, 2016

AMS Subject Classification: 30C45, 30C55

Key Words and Phrases: fractional calculus, analytic functions, unit disk, univalent functions, fractional differential operator, integral operator

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DOI: 10.12732/ijpam.v108i4.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 4
Pages: 781 - 790


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